Cost-optimized Automated Variance Reduction for Highly Angle-dependent Radiation Transport Analyses

Abstract

Monte Carlo variance-reduction techniques that directly bias particle direction have historically received limited attention despite being useful for many radiation transport applications such as those in which radiation travels through large regions with a low probability of colliding. One such technique is known as DXTRAN (short for deterministic transport) in the MCNP Monte Carlo radiation transport code. Until now, effectively applying DXTRAN in calculations is largely based on empirical observations of computational performance. Optimal DXTRAN parameters are identified through manual iteration. This work develops new mathematical descriptions of the DXTRAN variance-reduction process and demonstrates a new automated variance-reduction method that applies these mathematical formulations to determine the optimal application of DXTRAN in a given problem.

Specifically, this work includes the first known deduction and application of the integral transport kernels for both biasing with DXTRAN particle production and the associated free-flight transport with truncation of the initiating particle. This work applies these new DXTRAN transport kernels to derive expressions for the mean tally response in Monte Carlo transport calculations involving DXTRAN. These expressions are then used to rigorously prove, for the first time, that the technique is unbiased. This work also derives equations for the variance and associated computational cost of Monte Carlo calculations involving DXTRAN, which are solved using the deterministic discrete ordinates method.

To verify the derivations developed in this work, fourteen 1-D and seven 2-D test case calculations are made. Within the 2-D test cases, a variety of scenarios are examined that lead to highly angle dependent solutions where other variance-reduction techniques that do not directly bias particle direction are challenged. For the 1-D cases, when DXTRAN is solely used, the Monte Carlo and deterministically calculated mean and variances agree within 1.4%. For the 2-D cases, the agreement is generally well within 10% and never worse than 13%, which is consistent with prior analyses for other variance-reduction techniques.

Of the verification test cases, six 1-D and six 2-D test cases are processed using an automated optimization workflow to determine optimal DXTRAN variance reduction parameters. As long as a non-trivial change in FOM is predicted by the optimizer, the optimizer identifies improved DXTRAN parameters relative to the initial guess in all but one case. For the 2-D test cases, a coarse angular quadrature is used to permit the optimization iterations to run quickly; however, the relative change in computational cost as a result of varying DXTRAN size, position, and rouletting parameters is adequately captured.

This work provides a method that could augment a strictly variance-reducing hybrid radiation transport method (e.g., FW-CADIS) to improve the efficiency of highly angle-dependent radiation transport analyses.